53.15 NormalSubgroupClasses

NormalSubgroupClasses( G, classes )

returns the normal subgroup of the group G that consists of the conjugacy classes whose positions are in the list classes.

If G.nsg does not contain the required normal subgroup, and if G contains the component G.normalSubgroups then the result and the group in G.normalSubgroups will be identical.

    gap> ccl:= ConjugacyClasses( S4 );
    [ ConjugacyClass( S4, IdAgWord ), ConjugacyClass( S4, d ), 
      ConjugacyClass( S4, b ), ConjugacyClass( S4, a ), 
      ConjugacyClass( S4, a*d ) ]
    gap> NormalSubgroupClasses( S4, [ 1, 2 ] );
    Subgroup( S4, [ c, d ] ) 

The list of classes corresponding to a normal subgroup is returned by ClassesNormalSubgroup. Previous Up Top Next
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